Modeling ultrashort electromagnetic pulses with a generalized Kadomtsev–Petviashvili equation

A. Hofstrand, J. V. Moloney

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

In this paper we derive a properly scaled model for the nonlinear propagation of intense, ultrashort, mid-infrared electromagnetic pulses (10–100 femtoseconds) through an arbitrary dispersive medium. The derivation results in a generalized Kadomtsev–Petviashvili (gKP) equation. In contrast to envelope-based models such as the Nonlinear Schrödinger (NLS) equation, the gKP equation describes the dynamics of the field's actual carrier wave. It is important to resolve these dynamics when modeling ultrashort pulses. We proceed by giving an original proof of sufficient conditions on the initial pulse for a singularity to form in the field after a finite propagation distance. The model is then numerically simulated in 2D using a spectral-solver with initial data and physical parameters highlighting our theoretical results.

Original languageEnglish (US)
Pages (from-to)51-58
Number of pages8
JournalPhysica D: Nonlinear Phenomena
Volume366
DOIs
StatePublished - Mar 1 2018

Keywords

  • Filamentation
  • Kadomtsev–Petviashvili equation
  • Nonlinear optics

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Condensed Matter Physics
  • Applied Mathematics

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